Hidetoshi Nishimori and Gerardo Ortiz
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into ...
More
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.Less
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0018
- Subject:
- Physics, Nuclear and Plasma Physics
This chapter derives formulas for gross sections of potential scattering, and shows their generalizations to nuclear reactions. A projection technique is introduced, which allows one to separate in ...
More
This chapter derives formulas for gross sections of potential scattering, and shows their generalizations to nuclear reactions. A projection technique is introduced, which allows one to separate in the T-matrix the part which varies smoothly in energy from that for resonances. For the latter, general expressions are deduced which involve partial and total widths. Non-hermitean Hamiltonians for the optical model are obtained by applying suitable energy averages. The doorway mechanism is explained by which the intermediate structure in the resonances can be understood: it employs widths for decays to the continuum and to the compound states. The statistical theory is addressed, for which on the basis of general assumptions, analytic formulas for the fluctuating cross section are derived, which are in accord with N. Bohr's hypothesis of the independence of entrance and exit channels. The Weisskopf-Ewing relations and the Hauser-Feshbach theory are described, which involve branching ratios and formation probabilities. A critique of the statistical model is included.Less
This chapter derives formulas for gross sections of potential scattering, and shows their generalizations to nuclear reactions. A projection technique is introduced, which allows one to separate in the T-matrix the part which varies smoothly in energy from that for resonances. For the latter, general expressions are deduced which involve partial and total widths. Non-hermitean Hamiltonians for the optical model are obtained by applying suitable energy averages. The doorway mechanism is explained by which the intermediate structure in the resonances can be understood: it employs widths for decays to the continuum and to the compound states. The statistical theory is addressed, for which on the basis of general assumptions, analytic formulas for the fluctuating cross section are derived, which are in accord with N. Bohr's hypothesis of the independence of entrance and exit channels. The Weisskopf-Ewing relations and the Hauser-Feshbach theory are described, which involve branching ratios and formation probabilities. A critique of the statistical model is included.
ANDRÉ AUTHIER
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0014
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are ...
More
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.Less
This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.
Niels E. Henriksen and Flemming Y. Hansen
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199203864
- eISBN:
- 9780191708251
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199203864.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where ...
More
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.Less
This chapter considers unimolecular reactions; photo-induced reactions, i.e. true unimolecular reactions; and reactions initiated by collisional activation, i.e. apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, i.e. the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light, that is, laser control.
Jean Zinn-Justin
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed ...
More
This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed point, the Gaussian fixed point, which is stable in dimension larger than four. It identifies the leading perturbation to the Gaussian fixed point in dimension = four. It discusses the possible existence of a non-Gaussian fixed point near dimension four.Less
This chapter introduces the general concept of renormalization group in the spirit of the work. It studies the role of fixed points and their stability properties. It exhibits a particular fixed point, the Gaussian fixed point, which is stable in dimension larger than four. It identifies the leading perturbation to the Gaussian fixed point in dimension = four. It discusses the possible existence of a non-Gaussian fixed point near dimension four.
John von Neumann
Nicholas A. Wheeler (ed.)
- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780691178561
- eISBN:
- 9781400889921
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691178561.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, ...
More
This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ] (∥φ∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ] is the state φ).Less
This chapter provides the fundamental basis of the statistical theory, building on the formula introduced in the previous chapter, before elaborating proofs of the statistical formulas. From these, the chapter shows that the most general statistical ensemble which is compatible with the chapter's qualitative basic assumptions is characterized, according to 𝗧𝗿, by a definite operator 𝗨. Furthermore, those particular ensembles which have been called “homogeneous” were characterized by 𝗨 = 𝙋subscript [φ] (∥φ∥ = 1), and since these are the actual states of the systems 𝗦 (i.e., not capable of further resolution) they can also be called states (specifically, 𝗨 = 𝙋subscript [φ] is the state φ).
Jean Zinn-Justin
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199227198
- eISBN:
- 9780191711107
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227198.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter studies a statistical field theory with an O(N) orthogonal symmetry and a (f2)2 interaction (denoted here by f = (f1, . . . , fN) the N-component field rather than s, in contrast with ...
More
This chapter studies a statistical field theory with an O(N) orthogonal symmetry and a (f2)2 interaction (denoted here by f = (f1, . . . , fN) the N-component field rather than s, in contrast with previous chapters), at fixed dimension, in the framework of another approximation scheme, the N approaching the 8 limit. The results confirm the universal properties derived in the framework of the formal e-expansion.Less
This chapter studies a statistical field theory with an O(N) orthogonal symmetry and a (f2)2 interaction (denoted here by f = (f1, . . . , fN) the N-component field rather than s, in contrast with previous chapters), at fixed dimension, in the framework of another approximation scheme, the N approaching the 8 limit. The results confirm the universal properties derived in the framework of the formal e-expansion.
M. E. LINES and A. M. GLASS
- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198507789
- eISBN:
- 9780191709944
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507789.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book looks at some concepts leading to a basic understanding of ferroelectricity. Depending on their geometry, crystals are commonly classified into seven systems: triclinic (the least ...
More
This book looks at some concepts leading to a basic understanding of ferroelectricity. Depending on their geometry, crystals are commonly classified into seven systems: triclinic (the least symmetrical), monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. These systems can again be subdivided into point groups (crystal classes) according to their symmetry with respect to a point. There are 32 such crystal classes and 11 of them possess a centre of symmetry. Twenty of the 21 non-centric crystal classes exhibit electrical polarity when subjected to stress. The effect (and also its converse, the production of strain by application of an electric field) is linear, with reversal of the stimulus resulting in a reversal of the response, and is termed the piezoelectric effect. Topics in this book include statistical theory, soft modes, phase transitions, macroscopics and phenomenology, thermodynamics, structural crystallography, order-disorder ferroelectrics, nonlinear optics, and applications of ferroelectrics.Less
This book looks at some concepts leading to a basic understanding of ferroelectricity. Depending on their geometry, crystals are commonly classified into seven systems: triclinic (the least symmetrical), monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. These systems can again be subdivided into point groups (crystal classes) according to their symmetry with respect to a point. There are 32 such crystal classes and 11 of them possess a centre of symmetry. Twenty of the 21 non-centric crystal classes exhibit electrical polarity when subjected to stress. The effect (and also its converse, the production of strain by application of an electric field) is linear, with reversal of the stimulus resulting in a reversal of the response, and is termed the piezoelectric effect. Topics in this book include statistical theory, soft modes, phase transitions, macroscopics and phenomenology, thermodynamics, structural crystallography, order-disorder ferroelectrics, nonlinear optics, and applications of ferroelectrics.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0026
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
There is a rather subtle connection between quantum field theory and statistical physics, and this is explored here, where the concepts of imaginary time and the Wick rotation are introduced.
There is a rather subtle connection between quantum field theory and statistical physics, and this is explored here, where the concepts of imaginary time and the Wick rotation are introduced.
Niels Engholm Henriksen and Flemming Yssing Hansen
- Published in print:
- 2018
- Published Online:
- November 2018
- ISBN:
- 9780198805014
- eISBN:
- 9780191843129
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805014.003.0007
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter considers unimolecular reactions; photo-induced reactions, that is, true unimolecular reactions; and reactions initiated by collisional activation, that is, apparent unimolecular ...
More
This chapter considers unimolecular reactions; photo-induced reactions, that is, true unimolecular reactions; and reactions initiated by collisional activation, that is, apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, that is, the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light; that is, laser control.Less
This chapter considers unimolecular reactions; photo-induced reactions, that is, true unimolecular reactions; and reactions initiated by collisional activation, that is, apparent unimolecular reactions where it is assumed that the time scales for activation and subsequent reaction are well separated. Elements of classical and quantum dynamical descriptions are discussed, including Slater theory and the quantum mechanical description of photo-induced reactions. Statistical theories aiming at the calculation of micro-canonical as well as canonical rate constants are discussed, including a detailed discussion of RRKM theory. It concludes with a discussion of femtochemistry, that is, the observation and control of chemical dynamics using femtosecond pulses of electromagnetic radiation, focusing on the control of unimolecular reactions via the interaction with coherent light; that is, laser control.
